Calculating Oxygen Volume in Hospital Tanks Using Ideal Gas Law

[colton4286]

Oxygen for hospital patients is kept in special tanks, where the oxgen has a pressure of 65.0 atm and a temp. of 288 K. The tanks are stored in a separate room, and the oxygen is pumped to the patient's room, where it is administered at a pressure of 1.00 atm and a temp. of 297 K. What volume does 1.00 m^3 of oxygen in the tanks occupy at the conditions in the patient's room?

What I did was solve for the # of mols (n) given the tank information: n= PV/RT and used this n value to solve for volume: V= nRT/P. But I got 67 m^3 which is a much larger number than I expected. Am I heading in the right direction on this problem? Thanks!

 

[lzkelley]

That sounds exactly right.
Note that you don't actually have to solve for the number of moles, all you need to know is that it stays constant.

n = PV/RT and n is constant, therefore:
(PV/RT)1 = (PV/RT)2 where 1 and 2 correspond to before and after the pumping, i.e. 1 is at 65 atm 288K and 2 is at 1atm 297K.
Also R is constant, so you can cancel that out.

Cheers